Symmetry Breaking Predicates for SAT-based DFA Identification

It was shown before that the NP-hard problem of deterministic finite automata (DFA) identification can be effectively translated to Boolean satisfiability (SAT). Modern SAT-solvers can tackle hard DFA identification instances efficiently. We present a technique to reduce the problem search space by enforcing an enumeration of DFA states in depth-first search (DFS) or breadth-first search (BFS) order. We propose symmetry breaking predicates, which can be added to Boolean formulae representing various DFA identification problems. We show how to apply this technique to DFA identification from both noiseless and noisy data. Also we propose a method to identify all automata of the desired size. The proposed approach outperforms the current state-of-the-art DFASAT method for DFA identification from noiseless data. A big advantage of the proposed approach is that it allows to determine exactly the existence or non-existence of a solution of the noisy DFA identification problem unlike metaheuristic approaches such as genetic algorithms.